Video Lecture: Eigenvalues and vectors Rank: GATE 2017

Video Lecture: Eigenvalues and vectors Rank: GATE 2017








Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = −1. Then the eigenvalues of the matrix A19 are gatecs2012metrix
A
A
B
B
C
C
D
D
Answer: (D)

Explanation:
A =  1    1
     1   -1

A2 = 2   0
                0   2

A4 = A2 X A2
A4 = 4   0
                0   4

A8 = 16   0
                0    16


A16 = 256   0
                 0    256

A18 = A16 X A2
A18 = 512   0
                 0    512 

A19 = 512   512
                 512  -512


Applying Characteristic polynomial

512-lamda   512
512       -(512+lamda)  =   0

-(512-lamda)(512+lamda) - 512 x 512 = 0

lamda2 = 2 x 5122


Location: Pune, Maharashtra, India

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